Supersymmetric quantum theory, non-commutative geometry, and gravitation. Lecture Notes Les Houches 1995
arXiv:hep-th/9706132
Abstract
This is an expanded version of the notes to a course taught by the first author at the 1995 Les Houches Summer School. Constraints on a tentative reconciliation of quantum theory and general relativity are reviewed. It is explained what supersymmetric quantum theory teaches us about differential topology and geometry. Non-commutative differential topology and geometry are developed in some detail. As an example, the non-commutative torus is studied. An introduction to string theory and (atrix) models is provided, and it is outlined how tools of non-commutative geometry can be used to explore the geometry of string theory and conformal field theory.
143 pages, LaTeX file + 3 eps-figures
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- Brane Dynamics in Background Fluxes and Non-commutative Geometry
- Higher dimensional geometries related to fuzzy odd-dimensional spheres
- The Decay of Unstable Noncommutative Solitons
- On deformations of 2d SCFTs
- Algebraic backgrounds: a framework for noncommutative Kaluza-Klein theory